Curl of Vector Field and Path Integrals

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Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

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Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Taylor Polynomials and Function Properties

Covers Taylor polynomials, function properties, double integrals, partial derivatives, and function boundaries.

Vector Analysis: Basics and Applications

Explores the importance of vector analysis in physics and engineering, showcasing its application in various laws and relationships.

Derivable Functions: Partial Derivatives and Jacobian Matrix

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

Differentiability of Functions of Several Variables

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Time-dependent quantum mechanics: semiclassical atom-radiation interactions

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Vector Fields and Lorentz Tensors: Representation Theory

Covers the transformation properties of vector fields and their representation in Lorentz tensors.